Donald Trump and Hillary Clinton both racked up resounding victories on Tuesday night. Yet the closer the Republican and Democratic front-runners get to securing their respective party's presidential nomination, the more their primary opponents buckle down for a long fight.

Tuesday was perhaps the most important day for GOP front-runner so far. Trump secured three significant victories in Florida, Illinois and North Carolina while staying competitive in Ohio and Missouri. He managed to knock Sen. Marco Rubio out of the running while building up his biggest delegate lead to date.

Even so, the anti-Trump movement clinged to the hope they could find. Trump's most viable GOP opponent, Ted Cruz, couldn't win a single state on Tuesday, yet he sounded optimistic that his support will grow now that Rubio is out of the race. Ohio Gov. John Kasich, after losing 22 other nominating contests, pointed to his victory in his home state Tuesday night to justify his continued campaign.

John Kasich gets hometown win in Ohio

Kasich's victory in Ohio turns the race into a "whole new ballgame," Kasich's chief strategist John Weaver argued in a memo Tuesday night.

On the Democratic side, Hillary Clinton's success in at least four of the five contests Tuesday (with Missouri too close to call) helped widen her delegate lead and add to the perception that the Democratic nomination is ultimately hers. Vermont Sen. Bernie Sanders, by contrast, lost the opportunity to have the kind of surprise victory that reinvigorated his candidacy in Michigan last week.

Still, Sanders has given no indication that he's nearing the exits: in fact, at a rally in Phoenix Tuesday evening, he made no mention of the election results at all. And defeating him outright will be difficult for Clinton under the Democrats' delegate rules: unlike Republicans, who starting Tuesday allowed states to award their delegates on a winner-take-all basis, Democrats' delegates are awarded proportionally through the whole primary calendar.

Trump racks up delegates

On the Republican side, the math is a little more clear. After Tuesday, Trump has just about half the delegates he needs to win the nomination outright.

Donald Trump calls out attackers

The Kasich campaign's memo contends that the governor "is positioned to accumulate a large share of the almost 1,000 remaining delegates." Whether that's true or not, the fact of the matter is that Kasich won't win 1,237. In fact, he's so far behind with 136 delegates that he still has fewer than Marco Rubio (who exited the race with 164).

Cruz, meanwhile, pointed out Tuesday night that he and his supporters "continue to gain delegates and continue our march to 1,237." He failed to mention that Trump's single, winner-take-all victory in Florida gave Trump more delegates than Cruz collected in all of Tuesday night's races combined.

The best hope for the anti-Trump movement seems to be stopping the front-runner himself from reaching 1,237. Yet Tuesday night's events gave a taste of the sort of resentment that might generate among Republican voters. Trump supporters interrupted both Rubio's concession speech and Kasich's victory speech, showing just how zealously his supporters back his campaign.

Clinton cleans up

Clinton's near sweep of the evening should also serve as a wake-up call for her primary opponents. The night was a rebuttal of Sanders supporters' suggestion that Clinton can only win red or red-leaning states in the South: her first three victories of the night were in Ohio, Florida and North Carolina, all general-election swing states in different parts of the country. The former secretary of state's victory in Ohio was symbolically important in that it's the same kind of predominantly white, industrial state as Michigan, which Sanders won last week.

Hillary Clinton rebounds from Michigan loss with multiple wins.

In Florida, the first contest of the night to be called, Clinton defeated Sanders by 31 points (she won 64 percent of the vote, compared with 33 percent for Sanders). And in Ohio, where polls showed a single-digit race, Clinton's final margin of victory was 14 points (57 percent to 43 percent). Clinton pulled out a narrow victory in Illinois, defeating Sanders there by just one point, 50 percent to 49 percent.

After losing white voters 56 percent to 42 percent in Michigan last week, exit polling found Clinton winning white voters in Ohio by a 6-point margin, 53 percent to 47 percent. Clinton also won among white voters in Florida by 8 points, 52 percent to 44 percent. (Sanders won the white vote in the other three states: North Carolina, Illinois and Missouri.) Clinton also maintained her strong lead among Latino voters in Florida, where exit polling gave her a 72 percent to 28 percent advantage among the key demographic; the same was true of African-American voters in Ohio, which she won 70 percent to 28 percent.

While Clinton didn't explicitly suggest Sanders should exit the race --she said Tuesday that it's up to him to run his campaign how he wants -- Clinton spokesman Brian Fallon tweeted that Sanders is much further behind delegate-wise than Clinton ever was in 2008.

"Then-Sen Obama's largest lead over @HillaryClinton in 2008 was 157 pledged delegates," he tweeted. "After tonight, Clinton will lead by 300+ over Sanders."

Another Clinton backer, Correct the Record President Brad Woodhouse, put it this way: "Hillary Clinton's wins tonight effectively ended the Democratic nomination for president."

In her own remarks, Clinton seemingly made a bid for the small-dollar donors who have powered Sanders's impressive fundraising machine.

"If you've been waiting for the right moment," she told the crowd in Florida, "now's the time."